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North American Fuzzy Information Processing Society Annual Conference

NAFIPS 2017: Fuzzy Logic in Intelligent System Design pp 335–357Cite as

Intuitionistic Fuzzy Functional Differential Equations

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 648))

Abstract

In this paper, we discuss the local and global existence and uniqueness results for intuitionistic fuzzy functional differential equations. For the local existence and uniqueness we use the method of successive approximations and for global existence and uniqueness we use the contraction principle. Also we give an useful procedure to solve intuitionistic fuzzy functional differential equations. The applicability of the theoretical results is illustrated with some examples.

B. Ben Amma: Equal contributor.

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References

  1. Atanassov, K.: Intuitionistic fuzzy sets. VII ITKR’s session. Sofia (1983). (deposited in Central Science and Technical Library of the Bulgarian Academy of Sciences)

    Google Scholar 

  2. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MATH  Google Scholar 

  3. Atanassov, K.: Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 64, 159–174 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ben Amma, B., Melliani, S., Chadli, L.S.: Numerical solution of intuitionistic fuzzy differential equations by Euler and Taylor methods. Notes Intuit. Fuzzy Sets 22, 71–86 (2016)

    Google Scholar 

  5. Ben Amma, B., Melliani, S., Chadli, L.S.: Numerical solution of intuitionistic fuzzy differential equations by Adams three order predictor-corrector method. Notes Intuit. Fuzzy Sets 22, 47–69 (2016)

    Google Scholar 

  6. Ben Amma, B., Melliani, S., Chadli, L.S.: Numerical solution of intuitionistic fuzzy differential equations by Runge-Kutta Method of order four. Notes Intuit. Fuzzy Sets 22, 42–52 (2016)

    Google Scholar 

  7. De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117, 209–213 (2001)

    Article  MATH  Google Scholar 

  8. Kharal, A.: Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy 98, 35–39 (2009)

    Article  Google Scholar 

  9. Li, D.F., Cheng, C.T.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit. Lett. 23, 221–225 (2002)

    Article  MATH  Google Scholar 

  10. Li, D.F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70, 73–85 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1997)

    Google Scholar 

  12. Khastan, A., Nieto, J.J., Rodríguez-López, R.: Fuzzy delay differential equations under generalized differentiability. Inf. Sci. 275, 145–167 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lupulescu, V.: On a class of fuzzy functional differential equation. Fuzzy Sets Syst. 160, 1547–1562 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Melliani, S., Chadli, L.S.: Intuitionistic fuzzy differential equation. Notes Intuit. Fuzzy Sets 6, 37–41 (2000)

    MathSciNet  MATH  Google Scholar 

  15. Melliani, S., Elomari, M., Chadli, L.S., Ettoussi, R.: Intuitionistic fuzzy metric space. Notes Intuit. Fuzzy Sets 21, 43–53 (2015)

    Google Scholar 

  16. Melliani, S., Elomari, M., Chadli, L.S., Ettoussi, R.: Intuitionistic fuzzy fractional equation. Notes Intuit. Fuzzy Sets 21, 76–89 (2015)

    Google Scholar 

  17. Melliani, S., Elomari, M., Atraoui, M., Chadli, L.S.: Intuitionistic fuzzy differential equation with nonlocal condition. Notes Intuit. Fuzzy Sets 21, 58–68 (2015)

    Google Scholar 

  18. Shu, M.H., Cheng, C.H., Chang, J.R.: Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron. Reliab. 46, 2139–2148 (2006)

    Article  Google Scholar 

  19. Wang, Z., Li, K.W., Wang, W.: An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf. Sci. 179, 3026–3040 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ye, J.: Multicriteria fuzzy decision-making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment. Expert Syst. Appl. 36, 6899–6902 (2009)

    Article  Google Scholar 

  21. Zadeh, L.A.: Fuzzy set. Inf. Control 8, 338–353 (1956)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors would like to express our thanks to Professor Oscar Castillo for his valuable remarks concerning this work.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, 523, 23000, Beni Mellal, Morocco

    Bouchra Ben Amma, Said Melliani & L. S. Chadli

Authors
  1. Bouchra Ben Amma
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  2. Said Melliani
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  3. L. S. Chadli
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Corresponding author

Correspondence to Bouchra Ben Amma .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Reformat

  5. Laboratory of Computational Intelligence and Automation, University of Waterloo, Waterloo, Ontario, Canada

    William Melek

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Ben Amma, B., Melliani, S., Chadli, L.S. (2018). Intuitionistic Fuzzy Functional Differential Equations. In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_39

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  • DOI: https://doi.org/10.1007/978-3-319-67137-6_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67136-9

  • Online ISBN: 978-3-319-67137-6

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